06 loops 09 11 tủ tài liệu bách khoa

University
 of
 Washington
 

Compiling
 Loops
 
C/Java
 code:
 
while ( sum != 0 ) {
<loop body>

}

Machine
 code:
 
loopTop:

cmpl $0, %eax
je
loopDone
<loop body code>
jmp

loopTop

loopDone:

¢ 

How
 to
 compile
 other
 loops
 should

 be
 straigh  
§  The
 only
 slightly
 tricky
 part
 is
 to
 be
 sure

 where
 the
 condi6onal
 branch
 
occurs:
 top
 or
 bo8om
 of
 the
 loop

 

¢ 

How
 would
 for(i=0;
 i<100;
 i++)
 be
 implemented?
 

x86
 


University
 of
 Washington
 

“Do-­‐While”
 Loop

 Example
 
C
 Code
 

 int fact_do(int

Goto
 Version
 

 int fact_goto(int

x)

{

{

int result = 1;
do {
result *= x;
x = x-1;

} while (x > 1);
return result;

int result = 1;
loop:
result *= x;
x = x-1;
if (x > 1) goto loop;
return result;
}

}

¢ 
¢ 

x)

Use
 backward
 branch
 to
 conUnue
 looping

 
Only
 take
 branch
 when
 “while”
 condiUon
 holds
 
x86
 

University
 of
 Washington
 

“Do-­‐While”
 Loop
 CompilaUon
 
Goto
 Version

 
int
fact_goto(int x)
{
int result = 1;
loop:
result *= x;
x = x-1;
if (x > 1)
goto loop;
return result;
}

Assembly
 

 fact_goto:
pushl %ebp
movl %esp,%ebp
movl $1,%eax
movl 8(%ebp),%edx
.L11:
imull %edx,%eax
decl %edx

cmpl $1,%edx
jg .L11
movl %ebp,%esp
popl %ebp
ret

x86
 

Registers:
 
%edx

%eax

x
result

#
#
#
#

Setup
Setup

eax = 1
edx = x

#
#
#
#

result *= x
x-Compare x : 1
if > goto loop

# Finish
# Finish
# Finish


University
 of
 Washington
 

General
 “Do-­‐While”

 TranslaUon
 
Goto
 Version
 

C
 Code
 
do

¢ 

Body:
  {

 

 

 


 

¢ 

Body
 
while (Test);

}

loop:
Body
 
if (Test)

goto loop

Statement1;
 
Statement2;
 
…
 
Statementn;
 

Test

 returns
 integer
 
=
 0
 interpreted
 as
 false
≠
 0
 interpreted
 as

 true
 


 
 
x86
 


University
 of

 Washington
 

“While”
 Loop
 TranslaUon
 
C
 Code
 

 int fact_while(int

{

int result = 1;
while (x > 1) {
result *= x;
x = x-1;
};
return result;
}

Goto
 Version

 
x)

int fact_while_goto(int x)
{
int result = 1;
goto middle;
loop:
result *= x;
x = x-1;
middle:
if (x > 1)

goto loop;
return result;
}

Used
 by
 GCC
 for
 both
 IA32
 &
 x86-­‐64

 
¢  First
 iteraUon
 jumps
 over
 body
 computaUon
 within
 loop
 straight
 to
 test

 
¢ 

x86
 


University
 of
 Washington
 

“While”
 Loop
 Example
 
int fact_while(int x)
{
int result = 1;
while (x > 1) {
result *= x;
x--;
};
return result;

}

# x in %edx, result in %eax
jmp
.L34
#
goto Middle
.L35:
# Loop:
imull %edx, %eax #
result *= x
decl %edx

#
x-.L34:
# Middle:
cmpl $1, %edx
#
x:1
jg
.L35
#
if >, goto
#
Loop

x86
 


University
 of
 Washington
 

“For”
 Loop

 Example:
 Square-­‐and-­‐MulUply
 
/* Compute x raised to nonnegative power p */
int ipwr_for(int x, unsigned int p)
{
int result;
for (result = 1; p != 0; p = p>>1) {
if (p & 0x1)
result *= x;
x = x*x;
}

return result;
}
¢ 

Algorithm
 
§  Exploit
 bit
 representa6on:
 p = p0 + 2p1 + 22p2 + … 2n–1pn–1
 
§  Gives:

 xp = z0 · z1 2 · (z2 2) 2 · … · (…((zn –12) 2 )…) 2

zi = 1
 
 when
 pi = 0

zi = x when
 pi = 1
 
§  Complexity
 O(log p)

Example
 

n–1
 
 Umes
 

310
 =

 32
 *
 38
 

 =
 32
 *
 ((32)2)2
 

x86

 


University
 of
 Washington
 

ipwr
 ComputaUon
 
/* Compute x raised to nonnegative power p */

int ipwr_for(int x, unsigned int p)
{
int result;
for (result = 1; p != 0; p = p>>1) {
if (p & 0x1)
result *= x;
x = x*x;
}
return result;
}

before

 iteraUon
 
1
 
2
 
3
 
4
 
5
 

result

x=3

p=10

1
1
9
9
59049

3
9
81
6561
43046721

10=10102
5= 1012
2= 102
1=
12

02

x86
 


University
 of
 Washington
 

“For”

 Loop
 Example
 
int result;
for (result = 1; p != 0; p = p>>1)
{
if (p & 0x1)
result *= x;
x = x*x;
}
General
 Form

 

  for (Init; Test; Update)
Body
 
Init
 
result = 1

Test
 
p != 0

Update
 
p = p >> 1

Body
 
{
if (p & 0x1)
result *= x;
x = x*x;
}

x86
 


University
 of
 Washington
 

“For”→
 “While”

 
For
 Version
 

  for (Init; Test; Update
 )
Body
 
Goto
 Version
 

  Init;
goto middle;
loop:
Body
Update
 ;
middle:
if (Test)
goto loop;
done:

While
 Version
 

  Init;
while (Test
 ) {
Body
 
Update
 ;
 

}

x86
 


University
 of
 Washington
 

For-­‐Loop:

 CompilaUon
 
For
 Version
 

  for (Init; Test; Update
 )
Body
 

for (result = 1; p != 0; p = p>>1)

{
if (p & 0x1)
result *= x;
x = x*x;
}

Goto
 Version
 

  Init;
goto middle;

loop:
Body
Update
 ;
middle:
if (Test)
goto loop;
done:

result = 1;
goto middle;
loop:

if (p & 0x1)
result *= x;
x = x*x;
p = p >> 1;
middle:
if (p != 0)
goto loop;
done:
x86